Postnikov's divided symmetrization, introduced in the context of
volume polynomials of permutahedra, possesses a host of remarkable
``positivity'' properties. These turn out to be best understood
using a family of operators we call quasisymmetric...
In 2021 Avi gave a talk titled “Linear spaces of matrices” (see
https://www.youtube.com/watch?v=H1H0OkZfZXw).
As shown there, the study of linear spaces of matrices (which we
call matrix spaces) arises naturally (and independently) in many
different...
Originally introduced as analogs of symmetric spaces for
groups over non-archimedian fields buildings have proven useful in
various areas by now. In this talk I will introduce (Bruhat-Tits)
buildings, combinatorial toolkits to study them and
their...
A construction of Thurston assigns a hyperbolic 3-manifold to
any polyhedron; a natural question is: which such are arithmetic?
We report on ongoing work aiming to answer this question.
The ring of symmetric functions has a linear basis of Schur
functions sλ indexed by partitions λ=(λ1≥λ2≥…≥0).
Littlewood-Richardson coefficients cνλ,μ are the structure
constants of such a basis.
A function is Schur nonnegative if it is a linear...
A remarkable result of Brändén and Huh tells us that volume
polynomials of projective varieties are Lorentzian polynomials. The
dual notion of covolume polynomials was introduced by Aluffi by
considering the cohomology classes of subvarieties of a...
In this talk, I will discuss some results concerning the
geometry and topology of manifolds on which the first eigenvalue of
the operator -γΔ + Ric is bounded below. Here, γ is a positive
number, Δ is the Laplacian, and Ric denotes the pointwise...
